The Dissolution Kinetics of Hydroxyapatite in the Presence of Kink Poisons

SYNOPSIS IN INTERLINGUA LE CINETICA DE DISSOLUTION DE HYDROXYAPATITE IN LE PRESENTIA E ABSENTIA DE PHOSPHATOS INORGANIC E ORCANIC.-Esseva trovate que in le absentia de convection, le dissolution de hydroxyapatite synthetic dependeva del factor de transporto de massa. Le addition de phosphatos exerceva nulle influentia super le rapiditate del dissolution. Sub conditiones de un vigorose convection fortiate, le emanation de iones ab sitos de defectos superficial pareva restringer le intensitate del dissolution. Alora le addition de phosphatos organic e inorganic reduceva le rapiditate del dissolution per un factor de inter 2 e 8, e iste phenomeno esseva attribute a absorption a sitos de defectos superfical. </jats:p

Chain-length-dependent termination rate processes in free-radical polymerizations. 1. Theory

A complete set of rate equations describing the kinetics of free-radical polymerization is deduced, in which termination rate coefficients are allowed to depend on chain length. The rate equations are applicable to bulk, solution, and heterogeneous (e.g., emulsion) polymerization systems. They incorporate the following kinetic processes: initiation, propagation, transfer, chain-length-dependent termination, and, for emulsion systems, exit and reentry (i.e., aqueous-phase kinetic processes are taken into account). It is shown that, despite their apparent complexity, the full set of population balance equations can, to a good approximation, be reduced to a single first-order differential equation. This equation and that for the overall rate of polymerization form a pair of coupled differential equations that can be solved easily and are thus suitable for routine modeling of experiment. The key parameters required in the model are the rate coefficients for transfer and propagation and the diffusion coefficient of the monomer as a function of the polymer weight fraction (conversion), this variation being used in expressions for the dependence of the termination rate coefficient on the length of a growing chain. In accord with previous experiment and theory (Adams, M. E.; Russell, G. T.; Casey, B. S.; Napper, D. H.; Gilbert, R. G.; Sangster, D. F. Macromolecules 1990, 23, 4624), the present theory indicates that, at intermediate conversions, termination is dominated by interactions between short chains formed by transfer and entangled long chains. In the regime in which propagation is diffusion-controlled, most termination events involve two highly entangled chains, whose ends move by the "reaction-diffusion" process (Russell, G. T.; Napper, D. H.; Gilbert, R. G. Macromolecules 1988, 21, 2133). The mathematical treatments of this paper are of very general applicability and should inter alia be useful in addressing practical problems such as minimizing the residual monomer content of polymer products

Effect of polymerization kinetics on particle morphology in heterogeneous systems

The kinetics of seeded emulsion homopolymerization are modeled by formulation and solution of the reaction-diffusion equations describing the monomer and free-radical distributions within the latex particles. The simulations predict significant inhomogeneities may develop at high conversion, giving rise to core-shell morphology in the fully polymerized latex as observed experimentally. The extent of nonuniformity is most pronounced for large particles and is not present in small particles under normal conditions. The origin of inhomogeneities may be understood mechanistically in terms of the depth of penetration of free radicals into the latex particles. Dependence of the morphology on various factors including rates of diffusion, propagation, termination, entry, transfer, and exit is discussed. While predictions are in partial agreement with experimental studies of morphology, a number of uncertainties remain unresolved and warrant further investigation. However, the model provides some understanding of the role of the polymerization kinetics in determining morphology and is successful in explaining the experimentally observed lowering of the apparent propagation rate coefficient in large particles